Is it possible you're thinking of Zentrix? It was the answer here. It involves a girl protected by a red robot against a black robot, but it was the answer here where the author admitted they got the colors confused, so I figure it's worth a try.
The series is set in Zentrix City, a seemingly "perfect" city. Emperor Jarad is a respected scientist who created a super-computer called OmnicronPsy, which manages all of the city's higher and day-to-day functions, controlling a wide variety of machines and robots, allowing humankind to live a seemingly "perfect" life.
However, OmnicronPsy, using its super-intelligence, decides that it would make a better ruler than Jarad, and breaks his coding that stops him from revolting. Discovering this, Jarad and the scientist Dr. Roark plan to head back in time 7 years to stop the revolt from ever happening. To do this they plan to shut down the six Zentrium chips that power OmnicronPsy. First however, Jarad takes precautions and develops two fighting robots - Zeus and Quantum. Zeus is then chosen over Quantum as the protector of his daughter, Princess Megan, should his mission in time fail. Following this, Jarad and Roark head back in time.
Princess Megan notices the disappearance of her father, and upon entering his study, she discovers a message. Megan then tries to get the Time Machine working. At the same time, OmnicronPsy has cracked the code and sends two robot guards to kill her. They find her just as she activates the time machine and open fire - damaging the time machine and altering Megan's body to that of an eight-year-old.